Continued Fraction for 4/15

Express 4/15 as a continued fraction

In decimal terms, = 0.26666666666667

Continued Fraction Table

Start	Integer	Decimal Portion Start - Integer	Reciprocal: 1 ÷ Decimal
0.26666666666667	0	0.267	3.7453
3.7453	3	0.745	1.3423
1.3423	1	0.342	2.924
2.924	2	0.924	1.0823
1.0823	1	0.082	12.1951
12.1951	12	0.195	5.1282
5.1282	5	0.128	7.8125
7.8125	7	0.813	1.23
1.23	1	0.23	4.3478
4.3478	4	0.348	2.8736
2.8736	2	0.874	1.1442
1.1442	1	0.144	6.9444
6.9444	6	0.944	1.0593
1.0593	1	0.059	16.9492
16.9492	16	0.949	1.0537
1.0537	1	0.054	18.5185
18.5185	18	0.519	1.9268
1.9268	1	0.927	1.0787
1.0787	1	0.079	12.6582
12.6582	12	0.658	1.5198
1.5198	1	0.52	1.9231
1.9231	1	0.923	1.0834
1.0834	1	0.083	12.0482
12.0482	12	0.048	20.8333
20.8333	20	0.833	1.2005
1.2005	1	0.201	4.9751
4.9751	4	0.975	1.0256
1.0256	1	0.026	38.4615
38.4615	38	0.462	2.1645
2.1645	2	0.165	6.0606
6.0606	6	0.061	16.3934
16.3934	16	0.393	2.5445
2.5445	2	0.545	1.8349
1.8349	1	0.835	1.1976
1.1976	1	0.198	5.0505
5.0505	5	0.051	19.6078
19.6078	19	0.608	1.6447
1.6447	1	0.645	1.5504
1.5504	1	0.55	1.8182
1.8182	1	0.818	1.2225
1.2225	1	0.223	4.4843
4.4843	4	0.484	2.0661
2.0661	2	0.066	15.1515
15.1515	15	0.152	6.5789
6.5789	6	0.579	1.7271
1.7271	1	0.727	1.3755
1.3755	1	0.376	2.6596
2.6596	2	0.66	1.5152
1.5152	1	0.515	1.9417
1.9417	1	0.942	1.0616
1.0616	1	0.062	16.129
16.129	16	0.129	7.7519
7.7519	7	0.752	1.3298
1.3298	1	0.33	3.0303
3.0303	3	0.03	33.3333
33.3333	33	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003

Stop when the difference portion = 0

Use the Integer Column

[0; 3, 1, 2, 1, 12, 5, 7, 1, 4, 2, 1, 6, 1, 16, 1, 18, 1, 1, 12, 1, 1, 1, 12, 20, 1, 4, 1, 38, 2, 6, 16, 2, 1, 1, 5, 19, 1, 1, 1, 1, 4, 2, 15, 6, 1, 1, 2, 1, 1, 1, 16, 7, 1, 3, 33, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333]

What is the Answer?

How does the Continued Fraction Calculator work?

Free Continued Fraction Calculator - Shows the continued fraction for a fraction
This calculator has 1 input.

What 2 formulas are used for the Continued Fraction Calculator?

Decimal Portion = Start - Integer
Reciprocal = 1 / Decimal Portion

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Continued Fraction Calculator?

continued fraction: a fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose numerator is an integer and whose denominator is an integer plus a fraction and so on
decimal: Number in the form a/b where the result is not a whole number
fraction: how many parts of a certain size exist
a/b where a is the numerator and b is the denominator
integer: a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...

Example calculations for the Continued Fraction Calculator

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